Natasha Richardson, a member of the Redgrave acting dynasty and whose career highlights included winning a Tony award for a stage revival of Cabaret, has died following a skiing accident.

The 45-year-old star died at a hospital in New York after suffering a serious head injury in a fall at the Canadian ski resort of Mont Tremblant, near Montreal.

A statement released on behalf of the family by her husband's Los Angeles agent, Alan Nierob, said: "Liam Neeson, his sons, and the entire family are shocked and devastated by the tragic death of their beloved Natasha. They are profoundly grateful for the support, love and prayers of everyone, and ask for privacy during this very difficult time."

Members of her family including her two sons, Micheál and Daniel, her husband and her mother, Vanessa Redgrave, and her sister, Joely Richardson, had gathered at her hospital bedside after she was transferred from Canada to Lenox Hill hospital in New York.

Family members had been seen coming and going from the New York hospital since Tuesday. Vanessa Redgrave, Richardson's mother, arrived in a car with darkened windows and was taken through a garage when she arrived at the hospital on Manhattan's Upper East Side about 5pm on Wednesday.

An hour earlier, Joely Richardson arrived alone amid a swarm of photographers as she entered through the back of the hospital.Neeson left the hospital in the back seat of a black people carrier at about 8.30pm local time (1.30am GMT).

Richardson had fallen on a beginners' ski slope on Monday in an accident that had seemed innocuous at the time, even though she wasn't wearing a helmet. She had been with her sons Micheál, 13, and Daniel, 12, when they left the Hotel Quintessence and set off for a ski lesson.

Richardson was at the bottom of the slope in the mid-afternoon when she lost her balance and nosedived down the hill. She did not hit anyone or anything before coming to a stop, according to a resort spokeswoman, Catherine Lacasse.

Ski instructors who were with her at the time said she had laughed off the fall and insisted she was fine before returning to her room. She showed no external sign of injury or bleeding.

"She was laughing and joking and she walked to her room on her own," Lacasse told the Montreal Gazette on TuesdayTwo ski patrollers stayed with Richardson but after an hour she began complaining of a headache and was taken to the Centre Hospitalier Laurentien, not far from the resort.

Another Canadian newspaper, the Globe and Mail, has since reported that an ambulance requested by the ski patrollers was turned away. Yves Coderre , director of operations at Ambulances Radisson , said paramedics who responded were told they were not needed. "They never saw the patient. So they turned around."

Coderre said another ambulance was called later to the hotel by which time Richardson's condition was worse and she was rushed to the local hospital. She was later transferred to the intensive care unit at Sacré-Coeur hospital in Montreal and then flown to New York.

Neeson had flown from filming in Toronto to be at her side following the accident.

Richardson was flown home to New York on Tuesday night on a life-­support machine and taken to Lenox Hill.

Richardson was a member of a great theatrical dynasty. Her father was the late director Tony Richardson. She was also the granddaughter of Sir Michael Redgrave and Rachel Kempson, and the niece of Lynn Redgrave.

Born in May 1963, Richardson was educated at St Paul's Girls School in London and trained at London's Central School of Speech and Drama. By her early 20s she was an experienced stage actress, appearing in On the Razzle, Charley's Aunt and The Seagull, for which the London Drama Critics awarded her most promising newcomer.

Richardson appeared in several Hollywood films, notably in the lead role of Paul Schrader's Patty Hearst, although was best known for her work on the stage.

Although Richardson never shared her mother's fiercely expressed political views, they were close professionally and acted together, most recently on Broadway to play the roles of mother and daughter in a one-night benefit concert version of A Little Night Music, the Stephen ­Sondheim-Hugh Wheeler musical.

Before meeting Neeson (who called her "Tash"), Richardson was married to theatre producer Robert Fox.

She sometimes remarked on the ­differences between her and her second husband: she from a theatrical dynasty and he from a working-class background in Northern Ireland.

In 1986, she won the London Drama Critics' most promising newcomer award for her performance as Nina in The Seagull, alongside her mother.

Richardson won the Tony award for best actress in a musical for her performance as Sally Bowles in Sam Mendes' production of Cabaret on Broadway in 1998.

She married Neeson, the star of Schindler's List, in 1994 after the pair met on the set of the film Nell.

Natasha Richardson was also on the board of the US-based charity amfAR, The Foundation for Aids Research.

A spokeswoman for the charity said: "This is a catastrophic loss for the family and it is a terrible loss for amfAR and the fight against Aids.

"Natasha Richardson was a dedicated Aids advocate and an eloquent spokesperson for amfAR.

"She generously contributed her time and resources to amfAR for over 15 years."